I had no idea you could own somebody's name and signature. Why would you do that? Were they selling merch with his stamp on or something?
In this case it is for when you see products that contain a persons name or signature like a cologne, a watch or an item of clothing that is using a persons image. It can also extend to marketing and advertising as well as many other aspects.
Usually property rights are held by the person it is of (or who created it in terms of intellectual property) by default but you can either sell it or licence it, it is classed as property rights so it has to be conducted via contract which outline how it can and can not be used and for how long they have permission to use it for. A name and signature is unusual to be held by some who it hasn't originated from, but for people working in the public eye that are an employee of a company and feature in advertising it is normal to have some sort of image rights held by another party.
It usually isn't really that much of an issue, the only issue arises if United must own the name and unwilling to pay what Chelsea would like for it, unprepared to licence it (assuming Chelsea have rights to licence it) or Chelsea tell United to do one. All of which would be highly unusual because it is simple to work out a price that all parties benefit from.
The whole sponsorship stuff shouldn't be an issue either, it is no different than why you see players with boots by Nike but playing in a kit by Adidas. It is why certain players don't appear in certain types of marketing like club kit launches but will for their nations kit launch because it is by the manufacturer that sponsors them and the club kit isn't. If United however have it written into the contract that the manager will be part of it then they're daft as that makes things very difficult, but not impossible just expensive.
The whole thing is a bit blown out of proportion really especially as it certainly isn't United's first time dealing with this sort of thing and are well known for there expertise in this area. They were doing this before it was a norm in the industry.